We've been giving her cash each week and we have to physically take the vehicle to the gas station every weekend to fill it up (we don't pay cash at gas stations). Neither is particularly convenient for us.

Why don't you give her cash so she can go fill up the car herself, I'm wondering what your issue is with paying cash at a gas station?

It used to be possible to add a child to one's credit card - I don't know if that's still a possibility.

I would be leery of co-signing for a credit card unless you could unilaterally close the account if she starts overspending (and I have doubts a co-signer would be able to do that). As a co-signer you're responsible for her debt if she doesn't pay. Even if there is a beginning credit limit, that doesn't mean a cc company won't let someone charge above that limit - and jack up the interest rate when they do. And if she starts overspending and you can't close the account on your own, than you're stuck.

And I think co-signing on a cc teaches a teen a bad lesson that it's OK to co-sign for a close relative - I knew a couple women when I was in my 20's who co-signed (and got stuck with debt) credit cards for their boyfriends.

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